Hoàng's 3-divisibility conjecture for even-hole-free graphs

Let a hole be a chordless cycle of length at least four; it is even if its length is even. For an integer $k\geqslant 2$, a graph $G$ with at least one edge is $k$-divisible if, for every induced subgraph $H$ with at least one edge, $V(H)$ can be partitioned into $k$ sets, none of which contains a maximum clique of $H$. Hoàng's conjecture. Every even-hole-free graph is $3$-divisible. This conjecture concerns structural decompositions of even-hole-free graphs and the resulting chromatic bounds; the supplied text gives no resolution, so its status remains open.